Nuprl Lemma : system-equiv-is-equiv
∀[M:Type ⟶ Type]. EquivRel(System(P.M[P]);S1,S2.system-equiv(P.M[P];S1;S2)) supposing Continuous+(P.M[P])
Proof
Definitions occuring in Statement :
system-equiv: system-equiv(T.M[T];S1;S2),
System: System(P.M[P]),
equiv_rel: EquivRel(T;x,y.E[x; y]),
strong-type-continuous: Continuous+(T.F[T]),
uimplies: b supposing a,
uall: ∀[x:A]. B[x],
so_apply: x[s],
function: x:A ⟶ B[x],
universe: Type
Definitions unfolded in proof :
uall: ∀[x:A]. B[x],
uimplies: b supposing a,
member: t ∈ T,
strong-type-continuous: Continuous+(T.F[T]),
ext-eq: A ≡ B,
and: P ∧ Q,
subtype_rel: A ⊆r B,
equiv_rel: EquivRel(T;x,y.E[x; y]),
refl: Refl(T;x,y.E[x; y]),
all: ∀x:A. B[x],
System: System(P.M[P]),
system-equiv: system-equiv(T.M[T];S1;S2),
cand: A c∧ B,
so_lambda: λ2x.t[x],
so_apply: x[s],
implies: P ⇒ Q,
int_seg: {i..j-},
lelt: i ≤ j < k,
component: component(P.M[P]),
sym: Sym(T;x,y.E[x; y]),
trans: Trans(T;x,y.E[x; y]),
decidable: Dec(P),
or: P ∨ Q,
satisfiable_int_formula: satisfiable_int_formula(fmla),
exists: ∃x:A. B[x],
false: False,
not: ¬A,
top: Top,
prop: ℙ,
le: A ≤ B,
less_than: a < b,
guard: {T},
process-equiv: process-equiv
Latex:
\mforall{}[M:Type {}\mrightarrow{} Type]
EquivRel(System(P.M[P]);S1,S2.system-equiv(P.M[P];S1;S2)) supposing Continuous+(P.M[P])
Date html generated:
2016_05_17-AM-10_37_10
Last ObjectModification:
2016_01_18-AM-00_18_44
Theory : process-model
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